


Galois Theory

by primeideal



Category: Austin & Murry-O'Keefe Families - Madeleine L'Engle, Kairos (O'Keefe) Series - Madeleine L'Engle
Genre: 5 Things, Gen, Mathematics, Yuletide 2012
Language: English
Status: Completed
Published: 2012-12-18
Updated: 2012-12-18
Packaged: 2017-11-21 11:42:16
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 5,337
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/597350
Author URL: https://archiveofourown.org/users/primeideal/pseuds/primeideal
Summary: <blockquote class="userstuff">
              <p>Five times everything fell into place.</p>
            </blockquote>





	Galois Theory

**Author's Note:**

  * For [wei](https://archiveofourown.org/users/wei/gifts).



> Thanks to pressdbtwnpages for betaing! And to the #yuletide chatters for encouraging me on structure.

The question was simple.

“How was school?”

Charles Wallace Murry swung his legs back and forth in his seat, nibbling at his sandwich. “All right.”

“All _right_?” Meg echoed. “What happened?”

“Not...much. My classmates were a little disappointed that I didn't bring Louise again.”

“Again?”

“They liked her, I think, more than they like me. I told them she was the twins', more than mine. That's adapting, isn't it?”

“What?”

“I could've explained she's her own person, she doesn't really _belong_ to the twins. But she is theirs more than she's mine. That's easier for my classmates, don't you think?”

“I think so. Are you going to finish your sandwich? You need to get your strength back.”

“Eventually,” said Charles Wallace, peeling off the crust.

“How's Mr. Jenkins? Did you see him?”

“Not today. I tried to kythe, but he wasn't listening. He felt afraid.”

“He didn't kythe back to you...then how do you know how he felt?”

“Intuition. But I think this is progress. Before, he wouldn't have let on even that much.”

“Before, he didn't know what kything was. Do you need some milk?”

“I know where to find it, if I do. I wish I could talk to him, tell him not to worry.”

“He's in your school.”

“That's true, but I don't want to go try and talk to him. Not if it'll make me look too strange, to the other children.”

“Just give him time. He was scared about you too.”

“And even if _someone_ is scared about me, that doesn't mean they need to get me milk.” Charles Wallace hopped down out of the chair, collecting his sandwich off the table and, with a pointed effort, crammed the last bite into his mouth as he carried the empty plate to the sink.

“I can't help it,” said Meg, “you did have us all worried.”

He turned back from the sink and looked at her. “Meg.”

And she knew, somehow, that he did not want her to speak, so she gazed back at him and tried to connect. Outside, the frost had set in, covering each ghostly blade of grass, and she felt his focus as he tried to apprehend the scale of the faint remnants of life beyond them.

“No use,” he said, blinking, “not right now, we're close enough as it is.”

She nodded. “Don't strain yourself.”

“I'm fine,” he said again, but a little more gently.

And so he went back to school, and Meg tried not to interrupt him too much. Once in a while she would start the kythe, open herself first, but she wasn't sure whose sake she was doing it for and she let him be.

He would come up to her room in the attic when she needed him to. When Father was busy tinkering with his physics but seemed afraid, as if the fear of being lost in another world again was holding him back. When Calvin was busy playing basketball, doing something that made him “more him” and joyful, but too absorbed in the moment, in the strength of his teammates, in the motion of his own body, to reach out for her. When she was doing mathematics and one moment at peace, caught up in the equations that chimed correctly no matter the scale or the place or the time, and the next moment frustrated, stymied, fearing for some threat or another to the world when she wasn't even strong enough to make sense of equations that would never be useful to anyone anyway. Then Charles Wallace would be there, and she didn't need to have a word for kything.

But whether she called it that or not, she didn't fall out of practice right away. The moment came when she _did_ feel a wave of fear that she knew, without knowing how she knew, had to be Mr. Jenkins.

“Do you think he's all right?” she asked Charles Wallace.

He didn't have to ask who she meant. “Yes, I think so. People get afraid all the time, even of wonderful things.”

“Are you going to talk to him?”

“Me? No more than usual.”

“Usual?”

“He came to our class, about a week after I got better. After Louise—some of the other students were wondering what kinds of animals we can bring into class. He said that depending on how things went, maybe we'd be able to take a field trip. Go down into the city, see a zoo.”

“And how are things going?”

“Pretty well. I'm trying to learn more about other animals—earthling ones, I mean, so we have something to talk about. My classmates are surprisingly interested in biology, as long as I don't call it that.”

Meg nodded. “But what about Mr. Jenkins?”

“That, I don't know. I think you'd better be the one to talk to him.”

“That'll go well, I'm sure. Let's see if Dr. Louise would do it. She's an adult, she can relate to him better.”

“He chose to work with lots of children, though. You don't need to be an adult.”

“I don't think I even remember his first name.”

“We can find out—”

“I _Named_ him! And I don't even know who he is, really.”

Charles Wallace said nothing, but she seemed to hear, with the suddenness of a flame leaping from one piece of wood to the next, _you do know enough._

And so the next day Meg found herself cutting class, vaguely guilty about not being there, and hoping Calvin would help her catch up. As she stood outside Mr. Jenkins' office she felt at first a wild panic that he wouldn't be there, that he'd have gone to talk to the teachers or students or do something helpful—but no, there he was, drumming his fingers against a file cabinet.

“You,” he said, sounding more tired than surprised to see her. “What do you want?”

“Excuse me for dropping in...”

“Is your brother all right?”

“He's fine. How are you?”

“How am I?” he repeated. “I'm here, aren't I? Not too large, not too small.” The words sounded meaningless, and she stared at him unsure if he was mocking her. When she said nothing, he repeated, “What do you _want_?”

“I wanted to see if you were all right,” Meg stammered.

“Has anything—strange—come up?”

“No, not since Charles Wallace got better. He says you talked to his class.”

“A little bit. Not too much. I don't want to single him out specifically.”

“And I think he appreciates that. Thank you.”

“So then what brings you here?”

“Has there been anything strange for you? I'm sorry, I should have asked.”

“Nothing that seems wrong. But I can't be sure.”

“Anything seeming _righter_ than usual?”

“Nothing. Nothing at all, it's just gone back to—” He waved his hands over the desk. “Normal. But I suppose that's no more than I deserve.”

Two flashes of kything. Mr. Jenkins' desk—the pens, the envelopes, the accumulating weight of paperwork. She saw it as he did, knew the ridges and the compartments, understood the system he'd begun to sort things neatly and then abandoned in futility.

And, at the same time, a clear night at the star-watching walk, her and Charles Wallace and Fortinbras panting between them, lolling his tongue towards the starlight.

And the moments blurred—Fortinbras was _itchy_ and uncomfortably hot, his fur smelled, and there on the letterhead of the preprinted header was _Anthony_. Mr. Jenkins' name.

“How do you trust me?” he was saying.

“Sorry, what?”

“ _I_ know I'm me, that I'm not one of those...Echthroi. But you can't—you can't be sure this is the way things were supposed to turn out, is it?”

“There isn't _one_ way everything's supposed to be.” She tried to open her mind to Calvin, reach from the memories they shared. “There's enough freedom for things to change.”

“Pro—the cherubim is gone. And I'm just supposed to—not supposed—I'm still here, going back to this, like nothing's changed?”

“There might be more for you. Charles Wallace and Calvin and I—we've been—far away before. You might be called on for something else.”

“I don't know whether I'd want that or not.”

“If you were, you'd be all right. Look at me, I'm—”

 _Meg_ , Calvin would have said, _you're brilliant._

“I'm getting comfortable with it. Not _used_ to it, in the sense of tired of the wonder. But if you had to do something like that again, you'd be able to.”

“What about your brother?”

“He's not used to it either,” she said, surprising herself with the answer, “but he's also not really used to school, so you'd never know the difference.”

Mr. Jenkins—Anthony—nodded. “It's just, I don't know where to begin.”

“You were a teacher, right? Before being a principal?”

“Yes.”

“So start there. Start with what makes you—the most you. I guess.”

He nodded again. “I'll try. But sometimes I feel like I need other people to _make_ me myself.”

“You're a Teacher,” she repeated. “I suppose you need students.”

“And speaking of students—”

“I get it,” she cut him off, “I'm going to class.”

She kept herself open, as much as she could. And when she didn't sense any more fear coming from Anthony Jenkins, instead of believing it was her own weakness, she decided he had found another way to speak.

* * *

_Seven years later_

The trees stood short but proud, not quite ready for splitting.

“Hey, stand over here a minute.”

“What?”

“Just try and stare at them straight-on, get a flat view of things.”

“What are you doing?”

“Look, mine are bigger.”

“What?”

“The trees,” said Dennys smugly, waving at the grove of small Christmas trees. “The ones on my half are bigger.”

Sandy paused, squinting as he looked from one side to the other. “You're ridiculous.”

“A little bit.”

“We didn't even have halves, did we? They're just all our trees.”

“I'm pretty sure we did.”

“Even if we had, they all look about the same size.”

“You're just jealous.”

“You're just a goof.”

“Perhaps.”

“Seriously, you haven't been back any longer than I have, it's not like you've been able to water these any more...”

“Whoa, there.” Dennys held up a playful hand. “Don't you go all scientific-method on me, save that for the family.”

“Hey, you're the pre-med.”

“Yes, and I am extremely happy to be _home_ on _vacation_ where I don't have to memorize O-Chem.”

“Not my fault you couldn't make the exciting pre-law cut.”

“What classes do you even take?”

“I'm technically a political science major, but once I get those requirements out of the way I'm probably going to take philosophy too.”

“Oh, yes, very scientifically rigorous.”

“Shut up. Besides, I have time to take classes I actually like.”

“Like what, theory and practice of basketball?”

“Close. Music theory.”

“Is that any good?”

“I love it. Although there's some kind of mathy stuff about the tuning. All those circle-of-fifths things we had to learn for orchestra?”

“Yeah.”

“They don't really add up—twelve perfect fifths _can't_ equal some perfect number of octaves. It's something about logarithms and numbers not dividing into each other.”

“They can't? What was the point of all those tune-ups?”

Sandy grinned. “It's close enough for our ears.”

“Did the ancient Greeks know that? Protagoras or whoever was going on about the harmonies of everything?”

“Protogoras is from philosophy, so, probably not.”

“Shut up,” Dennis echoed, and the twins laughed.

“You must have time for some electives.”

“We don't call them 'electives,' we call them 'distribution requirements'.”

“Well, la-di-dah. Anything good?”

“Let's see, uh, nineteenth-century American literature. _Portrait of a Lady_ , _The Scarlet Letter_ , _The Horn of Joy._..”

“Sequels, _The Bassoon of Peace_ and _The Trumpet of Hope_?”

“Very funny. No, it wasn't actually that great, something about the past and future meeting...didn't make sense.”

“Yeah, that sounds really implausible,” Sandy said, a hint of impatience in his voice.

Dennys met his eyes wordlessly; then, both twins pulled away and giggled nervously. “We should go in.”

“Yeah,” Sandy said tonelessly, and they paced back to the house.

Charles Wallace was inside having lunch. “Hello,” he said. “How are the trees coming?”

“Pretty well,” said Dennys.

Sandy opened the refrigerator and began rummaging inside. “I miss the vegetable garden.”

“I don't miss weeding.”

“True.”

“Hey, Charles, who's the Greek who went on about the harmonies of everything?”

“The what, now?” said Charles Wallace.

“Vibrating strings or whatever, some math or music stuff. Not Protagoras.”

“Oh, Pythagoras,” Charles Wallace smiled. “Why do you ask?”

“My music theory class was about how it doesn't exactly add up because of logarithms,” said Sandy. “Would he have known about that?”

“Logarithms? Irrational numbers? That's very unlikely.”

“Like I said.”

“They say he had one of his comrades killed for proving the square root of two was irrational—even something as straightforward as the ratio of the diagonal of a square to the length of the side wasn't a simple fraction. You need a larger set of numbers to include them all.”

“Okay, thanks,” said Dennys, with just enough of an emphasis that Charles Wallace smiled and turned back to his lunch.

Sandy got his leftovers and began warming them up, leaving the refrigerator door for Dennys to rummage through. There had been something—a horn—he wanted to ask whether Dennys was sure—

He blinked and turned back to his lunch, and no ideas took hold.

Not that day.

* * *

_Eleven months later_

Some changes could be radical.

Meg woke up late the day after Thanksgiving, the turkey or her exhaustion having let her sleep in. The snow was still on the ground, the sun reflecting off of it making it brighter than it would otherwise have been.

She slowly climbed downstairs. “How's it going?” she asked, cautious.

“Dad got M—Mom O'Keefe home, she was stable as of then,” said Dennys. It must have been the first time he'd called her that.

“And Mom is going to want you to start on the leftovers before you bring some back to Calvin,” said Sandy, waving at the table, “so get started.”

“Calvin,” said Meg. “Right. He hasn't called again, has he?”

“Nope,” said Dennys. “How's this one?”

He nodded down at her, and Meg smiled. “Quiet today. Probably tired after last night.”

“Aren't we all,” said Sandy. “I'm not kidding about the food, you'd better get started.”

“Is Charles Wallace still asleep?”

“Yeah. Okay, you don't have to ask again, I'll start eating,” she teased, but pretty soon she had dug in. After a small serving, she noted, “Ananda's probably going to want some too.”

“Mom already fed her,” said Dennys, “don't worry.”

“I...won't,” Meg trailed off.

They were still making their way through the food when Charles Wallace came downstairs and quietly dug in. “What can I say?” he shrugged, after realizing how many helpings he'd gone through. “Thanksgiving comes but once a year. Might as well live it up.”

“He's got a point,” said Sandy, coming back for more, “Not every day you can get someone else to cook for you. Well. Maybe _you_ can, we're stuck with the dining halls.”

“Maybe,” he said distantly.

Meg looked over at him and felt the kythe begin—it was in some sense easier without the fate of the world between them. “How long did last night take?”

“One night, of course.”

“But...” His memories shone clear, and she could not but trust them. “You were Within for months, years at a time.”

“And I was outside for a night. I'm still fifteen. Still me.”

“It's hard to believe, that it all happened like that—”

“Then don't. Nobody else knows, you don't have to.”

“But I _want_ to, that's the thing. That music—you remember what I mean, don't you?”

“This?” And he summoned up the memory of himself and Gaudior whirling past the stars, caught up in the harmonies echoing around them.

“Yes! Don't you see, I'd live through all of the bloodshed, all of the projections again to hear that music. Anyone would. It felt so beautiful—but I've heard Mrs. Whatsit sing, don't you understand? I hardly deserve to hear that, too—I can barely remember it. I was right before, I've settled for the adult world, I—”

“Meg. You know it's not a question of deserves.”

“I know,” she replied, and it was an old anger poking through. The old anger that told her, a decade before, she could not give up—if her mother could be beautiful and brilliant, so could she. “But it's hard—or Aunt Beast! How could I be so lucky, to hear Aunt Beast's music, and barely remember Gaudior this morning?”

“To hear what, now?”

“Aunt Beast's music. From Ixchel.”

“I don't know what you're talking about.”

“Yes you do! _You_ couldn't forget! We had rescued Father from Camazotz and—” She broke off. Of course.

“ _You_ had rescued Father,” Charles Wallace kythed, “and I was an arrogant child who didn't know his weaknesses.”

“Don't say that!”

“But you understand? The adult world has its advantages.”

“Are you going to have any more?” That was Sandy, talking in space and making sound.

Charles Wallace blinked. “Not right now, but maybe later. No telling what will have changed by dinner time.”

Meg glanced down at her stomach, and smiled up at her brothers. “Yeah.”

* * *

_Two years later_

Though they'd been very close growing up, the twins were facing adulthood and finding themselves separable.

By the time they had graduated from college, the Christmas trees were reaching a respectable height, though they'd need a couple more years to stop growing. Instead, the Murrys made do with a farmbought tree that Charles Wallace watered sporadically.

“I can't believe you're old enough to drive,” said Dennys.

“Dad drove. I don't have my license yet. But I picked it out,” said Charles Wallace.

“Yet?” said Sandy. “Are you going to get one?”

“Maybe. Someday,” he shrugged.

“All right. Well. Dennys, this is for you—” Sandy broke off as he looked more closely at the envelope in his hand. “Wait. What?”

“That's yours,” said Dennys, “has your name on it.”

Sandy ripped the envelope open and squinted at the piece of paper inside. _IOU Sox tickets sometime, maybe this summer if we can get standing-room tickets?_ “Thanks!” he said, but he didn't seem too enthused.

“What's wrong? You haven't become a Yankees fan, have you?”

“No—nothing—just—oh, let's have Polly open hers.”

With a little bit of guiding from her father, Polly successfully unwrapped some board books (from Charles Wallace), a stuffed bear (from Dennys), and a triangle (from Sandy, which she beat in impressive time to the Christmas hymns playing in the background).

As the pile of presents grew thinner, Dennys spied a thin envelope below the tree. “Hey, what's this? Sandy?”

Sandy raised his eyebrows but said nothing as Dennys ripped it open. _Celtics tickets maybe. Whenever we're both in Boston. Let me know._

And they burst out laughing. “Could be worse,” Dennys eventually shrugged, “we could have paid for the tickets and bought them for the same day.”

“Yeah, I guess.”

“Maybe just one game, it's cheaper. Considering how many years we're going to be racking up these student loans.”

Sandy shrugged. “Helps to have a Nobelist in your camp, just in case.”

Mrs. Murry laughed. “For my next investigation, I'll be researching claims of 'twin telepathy.' I hope you two are ready to sign a bunch of consent forms.”

“Oh, come on, Mom,” said Dennys, “surely as a scientist you know the odds of this happening among two New England sports fans—”

“—who were so busy they left it till the last minute—” Sandy added.

“—is actually decently high to begin with.”

“If it's all the same, Den, I hope you don't mind not being telepathic. I quite enjoy making up my own mind every once in a while.”

“No hard feelings. I know what you mean.” Dennys paused. “Poor choice of words?”

“Yes.”

Calvin was lighting candles, while Polly had clambered onto Charles Wallace's lap and was punctuating his reading of the book of John with her new triangle. _“In the beginning was the Word—”_ ding! “ _and we have seen his glory_ ”ding!“... _full of grace and truth.”_ ding!

“See,” Dennys pointed, “I would never give her something as potentially distracting, because I have taste.”

“Uh-huh,” said Sandy. “How's med school going?”

“Well, I don't want to brag, but I'm getting good grades. In spite of my professors' best efforts to present the material in some inaccessible way.”

“Already think you can do it better?”

“Today, sure. Hopefully by the time I'm done with school my brain won't have warped to the point that I think it makes sense. I want to get out there, start making a difference.”

“And leave future generations to your professors?”

“Hopefully they'll have retired by then.”

“Good luck with that.”

Dennys grinned. “And how's your school?”

“Not too bad. My professors aren't bad, it's just really hard, but I got a study group together.”

“Nice! So you just quiz people on stuff?”

“Oh, no, I'm not in charge—I mean, I just bribe people with food. And next year when I get the window box going hopefully I can bribe them with pretty flowers.”

“When you do what?”

“Didn't I tell you? I'm totally starting a window box, you know, to grow stuff from my apartment.”

“... _I_ was going to start a window box!”

“You're allowed!”

“Yeah, well, people are just going to accuse us of being telepathic again.”

 _Ding!_ went Polly's triangle.

“Oh, don't you start,” Dennys groaned.

“No, you should have your classmates over too,” said Sandy. “Look over the notes together. That way you can help them out and you don't have to talk at them like whatever the professors do. And if you're lucky maybe they'll start growing stuff too so you have a different view every once in a while.”

“Teaching by example. I like the sound of that.”

“You should, we're twins,” Sandy teased.

“Yeah, well,” he dropped his voice, “that doesn't mean I like the sound of the triangle.”

“Touché.”

* * *

 

_Six months later_

And every once in a while, even staying put felt transcendent.

Charles Wallace O'Keefe was born on the day his namesake graduated from high school, a continent away. Charles Wallace Murry was detached from the ceremony, going through the motions alongside his classmates but joining Meg and Calvin as they welcomed his nephew.

A few minutes afterwards, Meg held the newborn and wearily smiled. Next to her, Calvin tried to hold on to a squirming Polly. “Remember this,” kythed Charles Wallace. “This is the sort of moment other people from other worlds might visit, to learn joy from Earthlings.”

“We're naming him Charles,” Meg tried to explain.

“After his uncle,” said Calvin.

“That is an honor.” Charles Wallace paused. “I can't promise to always be there for him.”

“With my work, I haven't made that the easiest.”

“And with mine...well, never mind. Charles O'Keefe, you are welcomed and loved, wherever and whenever you and your family are.”

“He says 'wah,'” Meg contributed.

“I know he doesn't understand. That makes it all the more important, to talk to him anyway.”

“Have you decided about college?” said Calvin. “I know you were still thinking it over.”

“I'm going after all. Dad helped me figure it out. If I ever want to work for the government accreditation would be useful.”

“Well, I'm glad you've figured that out. You don't need us to tell you you'll do well.”

“I like the _idea._ Dad's coworkers were the ones who taught him about tessering. And it's thanks to that that we were able to hear about Mad Dog Branzillo in time.”

“You like the idea, and in practice?”

“Governments also make wars and waste resources.”

“Mom got her degrees and did something quite different with them,” Meg pointed out. “You have time.”

“That I do.”

“I think we need to rest,” said Calvin, “and you have a diploma of your own to celebrate.”

Meg caught a glimpse of Charles Wallace's private satisfaction—no great relief at checking off his academic boxes, but the accomplishment of making it through, of being able to stand alongside his classmates and not need to stand out, but also being able to be with his wider family. “We'll keep in touch, though,” she said.

And they did, Charles Wallace smiling when Calvin made progress on his research in—literally—bits and pieces. Polly and young Charles were every bit as distinctive and complex as anyone else, to him, as swift as the tiniest blood cell and as dependent as the most enormous moon.

“They can't recognize me in particular,” he kythed, “but they're loved by untold numbers of people they can't see.”

“It's not like they're actually—communicating with you, is it?” asked Meg.

“Not at all.”

“Don't you think kything comes to everyone naturally, we just grow out of it?”

“I don't think so, no. Babies are extremely...nearsighted.”

“You've always been special. I just—” She broke off, not sure what she was fearing. It was hard to understand inside herself, and harder still to let Charles Wallace feel.

“Meg, there's no shame in not knowing how to kythe. For humans? It's much harder than learning a second language. In the mesh of the universe there aren't very many creatures who can speak our languages, and they don't expect it of us.”

“Don't they, though? If anyone from a cherubim to a farandola knows how to kythe, it must be some sort of universal language.”

“Do you really believe that?”

“No. I just—people make so much of a deal about music and math, trying to describe them as some kind of universal languages instead of what they are, also powerful, also beautiful, but _different_.” She thought back to kything with Matthew Maddox, earning money through his stories to change the pulse of history.

“Yes, all right. And how is math going?”

“Oh, well enough. I'm working on some models of Calvin's stuff. He thinks—”

“—that yours are too theoretical and he should publish with a more accurate even if it's a less intuitive formula.”

“We've been in touch,” Calvin chimed in. “Tell him about your own work.”

“I don't want to jinx anything,” said Meg.

“Jinx anything?” Charles Wallace repeated.

“Everything's all bound up together, I can't help being superstitious if I mention things before they're set in stone.”

“Does this even count as a mention?” Calvin asked.

“Calvin, let her be,” Charles Wallace began.

But Meg interrupted. “No, I'm all right. I've been corresponding with a couple professors in the UK and writing some algebra papers. The first is in peer review but I'm hoping to have it published in a journal soon.”

“There've been a couple holdups,” said Calvin, “but I just like to think it's because Meg is peerless.”

“That's wonderful!” said Charles Wallace. “Send me a copy whenever it comes out, by normal mail, I want to read it.”

“ _If_ it comes out,” said Meg.

“What sort of algebra? Anything I'd have heard of?”

“Have you read about field theory?”

“Some. Not much.”

“Lucky you,” said Calvin, “she offers to explain it to me but there's no way I can keep up.”

“Oh, you can,” said Meg.

“What, you think by kythe it would be easier?”

“No, but—you've almost got it. I'll try again.”

“Don't let me keep you,” said Charles Wallace. “How late is it over there, anyway?”

“Not late at all, you're just up early.”

“Maybe you should check in later,” said Calvin. “Charles—our Charles—just woke up, we should probably check on some diapers.”

“Of course,” Charles Wallace replied, “good luck.”

While Charles the younger was content to nurse, Polly needed a diaper change, which Calvin attended to before sitting down next to Meg.

“Let's try this again,” she smiled. “You know about geometry—that if two sides of a right triangle are the same, the diagonal will be longer. The square root of two.”

“Right, yeah,” Calvin responded, “That's the Pythagorean theorem.”

“And of course, that's a length—a distance in space, it needs to be some positive number. It couldn't be less than zero.”

“A distance less than zero would just be silly. Unless that's some sort of tessering thing?”

“That doesn't matter, not really. But when you turn it into an algebra problem—you could say you're solving for x, such that x squared equals two.”

“So what?”

“So the algebra problem has another solution—the negative square root of two is just as valid an answer, since when you square it, a negative times a negative is a positive. You still get two. And once you _have_ the original answer you want, the positive number—you can't escape the negative root, just by multiplying by negative one, the second solution comes for free.”

“You need to take the negatives with the positives? That doesn't sound very inspiring.”

“See, _this_ is why we can't have math as the universal language, people read too much into it.”

“Do you need me to burp him?”

“I can do it,” said Meg, shifting Charles. “Okay. But once you've added on positive and negative square root of two to your set of fractions—you can add them to other numbers, multiply, divide, do whatever you want—you can interchange the positive and negative signs on these square-root-of-two components. Since as far as the original equation is concerned, x squared equals two, they behave the same way, you can swap out negative and positive terms and everything works out the same.”

“Even if it won't do you much good for actually finding distances.”

“Right. What's strange is that there's a deep symmetry—a correspondence between the subsets of numbers in question, and groups of functions from the set to itself. The ways in which you can move around in the sets while preserving everything that matters.”

“And that's what you study.”

“Well. 'Study.'”

“Research.”

“Yeah.”

“Are you still there?” Calvin kythed.

“Yes,” Charles Wallace responded.

“I think I get it this time. More so than usual. Which isn't much. Fields, is it?”

“Field theory,” Meg kythed back. “Well, Galois theory, but—”

“Galois theory?” Charles Wallace echoed.

Meg and Calvin both answered with two different versions of “What's wrong with that?”

“Nothing's _wrong_ with it, just—I didn't know that was what you were interested in.”

“I had a good algebra professor in college, that was what stuck with me.”

“What's a galois?” Calvin asked. “Some kind of square root?”

“No, a mathematician. Famous for coming up with these field ideas.”

“Also famous for dying in a duel at the age of twenty,” Charles Wallace contributed, “which hasn't done much to dispel the stereotype that mathematics is a young man's vocation.”

Calvin paused. “I didn't know.”

“No,” Meg rushed, “this area is beautiful for its own sake, not to—make a point—”

“I don't care! I can't keep up with any of your math anyway, it's no skin off my back whether you do algebra or—analysis, or topology or what have you.”

“No,” said Charles Wallace, “I shouldn't have—”

“It's all right,” said Meg. “Don't you see? It's _math_ , it doesn't matter who proves it or where, it's still true.”

“Or when,” said Charles Wallace. “When doesn't matter.”

She sat silently for a moment, then kythed back to him alone. “I'm a Namer. Charles Wallace was named after you, but we have other brothers, after all, and I think the next few will be named after them.”

“The next few?”

“I'm Mrs. O'Keefe, now, and if I have lots of kids, I'd like to make that name something to be proud of.”

And she sat with her husband by her side and her brother in her heart, holding her son in her arms and the equations in her mind.


End file.
